Yes, it does, it gives you extra damage depending on your furry's level. Mine gives me +82 damage, and it also gives you 50 mana and I think health, or maybe that's because of the iron armor.
If you want the Moon Katana Replica, I recommend you use a small, dirty trick: save after defeating the Homage until it drops the katana. It's a long process of saving and loading.But it will save you time, believe me.
Another thing that needs clarifying is that the katana is only given to you by that girl with pigtails and the katana, although you probably already know that, but it's always better to clarify, don't you think?